1933
This number is a prime.
In January 1933 Adolf Hitler was appointed chancellor of Germany and before August of the same year Germany was declared a one-party state.
The smallest prime (emirp) whose the sum and the product of
digits are equal to the same powers of consecutive primes
(16=2^4, 81=3^4). Note that the sum plus the product of
these digits is equal to the largest double-digit prime
(emirp). [Loungrides]
The only year of the 20th century to divide a repunit prime with no more than 21 digits: 111111111111111111111 = 3 * 37 * 43 * 239 * 1933 * 4649 * 10838689. It therefore divides the repunit prime with 2*21 = 42 digits. [Post]
Inauguration Day in the United States occurred on March 4
from 1798 up to the emirp year 1933 when Franklin D.
Roosevelt was inaugurated President. Since then
Inauguration Day has been on January 20. Furthermore, 3041933
(3/04/1933) is prime. [Green]
1933 = (19 + 28 + 37 +
46 + 55)/5. [Wesolowski]
The smallest happy balanced prime. [Gaydos]
The smallest Honaker prime with a Sophie Germain prime twin. [Gaydos]
1933 is the smallest prime whose sum of each digit raised to the same whole number is square. [Gaydos]
9331 is the smallest positive integer whose sum of divisors
(1933) is its prime anagram. [Gaydos]
The smallest prime obtained by concatenating all
(unordered) pairs whose product is a given number (9 in
this case): 1•9=3•3. [Leonardis]
Stanley Skewes in 1933 (assuming the Riemann Hypothesis)
was the first to give an explicit upper bound for Ξ. [Plymen]